document.write( "Question 1189525: What is the smallest positive multiple of 450 whose digits are all zeroes and ones?
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Algebra.Com's Answer #820902 by MathLover1(20850) $\"\"$ $\"About$

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the smallest positive multiple of $\"450\"$ whose digits are all $\"zeroes\"$ and $\"ones\"$ ?\r
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\n" ); document.write( "\n" ); document.write( "We know that it must be an $\"even\"$ multiple of $\"450\"$ . Otherwise the last two digits will be $\"50\"$ .\r
\n" ); document.write( "\n" ); document.write( "first multiple is $\"900\"$ \r
\n" ); document.write( "\n" ); document.write( "what is the smallest $\"positive\"$ multiple of $\"900\"$ such that all the digits are $\"0\"$ s or $\"1\"$ s?\r
\n" ); document.write( "\n" ); document.write( "apply a rule of multiples of $\"9\"$ : \r
\n" ); document.write( "\n" ); document.write( "the sum of the digits of a multiple of $\"9\"$ is a multiple of $\"9\"$ \r
\n" ); document.write( "\n" ); document.write( "This rule goes both ways. If the sum of the digits is a multiple of $\"9\"$ , the number is a multiple of $\"9\"$ .\r
\n" ); document.write( "\n" ); document.write( "That makes $\"11111111100\"$ our number.\r
\n" ); document.write( "\n" ); document.write( "check: $\"+450%2A24691358=+11111111100\"$ \r
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